arXiv subjects
Publications and source records attributed to K. G. Chetyrkin.
We report on some technical aspects of our calculation of alpha_s^4 corrections to R(s) and the semi-leptonic tau decay width [1-3]. We discuss the inner structure of the result as well as the issue of its correctness. We demonstrate recently appeared independent evidence positively testing one of two components of the full result.
We compute the form factors of the photon-quark-anti-quark vertex and the effective vertex of a Higgs boson and two gluons to three-loop order within massless perturbative Quantum Chromodynamics. These results provide building blocks for many third-order cross sections. Furthermore, this is the first calculation of complete three-loop vertex corrections.
In this paper we compute the three-loop corrections to the $β$ function in a momentum subtraction (MOM) scheme with a massive quark. The calculation is performed in the background field formalism applying asymptotic expansions for small and large momenta. Special emphasis is devoted to the relation between the coupling constant in the MOM and $\overline{\rm{MS}}$ schemes as well as their ability to describe the phenomenon of decoupling. It is demonstrated by an explicit comparison that the $\overline{\rm{MS}}$ scheme can be consistently used to relate the values of the MOM-scheme strong-coupling constant in the energy regions higher and lower than the massive-quark production threshold. This procedure obviates the necessity to know the full mass dependence of the MOM $β$ function and clearly demonstrates the equivalence of both schemes for the description of physics outside the threshold region.
We report on two recent results based on the evaluation of five-loop massless propagators in QCD and QED: (i) corrections of order $α_s^4$ to the absorptive part of the polarization function in QCD with $n_f=3$;(ii) the five-loop contribution to the $β$ function of quenched QED.
We use lattice QCD simulations, with MILC gluon configurations and HISQ c-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the MSbar mass of the charm quark and of the MSbar coupling. We find m_c(3GeV)=0.986(10)GeV, or, equivalently, m_c(m_c)=1.268(9)GeV, both for n_f=4 flavors; and alpha_msb(3GeV,n_f=4)=0.251(6), or, equivalently, alpha_\msb(M_Z,n_f=5)=0.1174(12). The new mass agrees well with results from continuum analyses of the vector correlator using experimental data for e+e- annihilation (instead of using lattice QCD simulations). These lattice and continuum results are the most accurate determinations to date of this mass. Ours is also one of the most accurate determinations of the QCD coupling by any method.
We report on two recent multiloop results in QED: (i) the four-loop corrections to the conversion relations between the QED charge renormalized in the on-shell and MS-bar schemes; (ii) analytical evaluation of a class of asymptotic contributions to the muon anomaly at five-loops.
Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alpha_s^4 for the cross section of electron-positron annihilation into hadrons and for the decay rates of the Z-boson and the tau-lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant alpha_s, as extracted from these measurements, and to a small shift of the central value, moving two central values closer together. The agreement between two values of alpha_s measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and tau decays we find alpha_s(M_Z)=0.1198 \pm 0.0015 as one of the most precise and presently only result for the strong coupling constant in order alpha_s^4.
We calculate the $O(α_s)$ and $O(α_s^2)$ gluon radiative corrections to the QCD sum rule for the first Gegenbauer moment $a_1^K$ of the kaon light-cone distribution amplitude. The NNL0 accuracy is achieved for the perturbative term and quark-condensate contributions to the sum rule. A complete factorization is implemented, removing logarithms of $s$-quark mass from the coefficients in the operator-product expansion. The sum rule with radiative corrections yields $a_1^K(1 \GeV)=0.10\pm 0.04$.
We present in analytic form the O(alpha_s^5) correction to the H->gg partial width of the standard-model Higgs boson with intermediate mass M_H<2M_t. Its knowledge is useful because the O(alpha_s^4) correction is sizeable (around 20%). For M_H=120 GeV, the resulting QCD correction factor reads 1 + (215/12) alpha_s^(5)(M_H)/pi + 152.5 (alpha_s^(5)(M_H)/pi)^2 + 381.5 (alpha_s^(5)(M_H)/pi)^3 \approx 1+0.65+0.20+0.02. The new four-loop correction increases the total Higgs-boson hadronic width by a small amount of order 1 promille and stabilizes significantly the residual scale dependence.
The four-loop QCD corrections to the electroweak $ρ$-parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing ``non-singlet'' piece. Using algebraic methods the amplitude is reduced to a set of around 50 new master integrals which are calculated with various analytical and numerical methods. Inclusion of the newly completed term halves the final value of the four-loop correction for the minimally renormalized top-quark mass. The predictions for the shift of the weak mixing angle and the W-boson mass is thus stabilized.
New results at four-loop order in perturbative QCD for the first two Taylor coefficients of the heavy quark vacuum polarization function are presented. They can be used to perform a precise determination of the charm- and bottom-quark mass. Implications for the value of the quark masses are briefly discussed.
It is shown that for every problem within dimensional regularization, using the Integration-By-Parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of dimension equal to four. We argue that the use of such a basis simplifies and stabilizes the numerical evaluation of the master integrals. As an example we explicitly construct the ep-finite basis for the set of all QED-like four-loop massive tadpoles. Using a semi-numerical approach based on Pade approximations we evaluate analytically the divergent and numerically the finite part of this set of master integrals. The calculations confirm the recent results of Schröder and Vuorinen. All the contributions found there by fitting the high precision numerical results have been confirmed by direct analytical calculation without using any numerical input.
We report about recent progress in computing four-loop massive correlators. The expansion of these correlators in the external momentum leads to vacuum integrals. The calculation of these vacuum integrals can be used to determine Taylor expansion coefficients of the vacuum polarization function and decoupling functions in perturbative Quantum chromodynamics. New results at four-loop order for the lowest Taylor expansion coefficient of the vacuum polarization function and for the decoupling relation are presented.
We include the new, five-loop, O(alpha_s^4) correction into the QCD sum rule used for the s-quark mass determination. The pseudoscalar Borel sum rule is taken as a study case. The OPE for the correlation function with N^4LO, O(alpha_s^4) accuracy in the perturbative part, and with dimension <= 6 operators reveals a good convergence. We observe a significant improvement of stability of the sum rule with respect to the variation of the renormalization scale after including the O(alpha_s^4) correction. We obtain the interval m_s(2 GeV)=105 \pm 6 \pm 7 MeV, which exhibits about 2 MeV increase of the central value, if the O(alpha_s^4) terms are removed.
We discuss recent developments in multiloop calculations aiming eventually in computing the total cross section for e^+e^- annihilation into hadrons in order alpha_s^4.
We compute, for the first time, the absorptive part of the massless correlator of two quark scalar currents in five loops. As physical applications we consider the O(alpha_s^4) corrections to the decay rate of the Standard Model Higgs boson into quarks, as well as the constraints on the strange quark mass following from QCD sum rules.
We present the matching condition for the strong coupling contant alpha_s at a heavy quark threshold to four loops in the modified minimal subtraction scheme. Our results lead to further decrease of the theoretical uncertainty of the evolution of the strong coupling constant through heavy quark thresholds. Using a low energy theorem we furthermore derive the effective coupling of the Higgs boson to gluons (induced by a virtual heavy quark) in four- and (partially) through five-loop approximation.
The first complete calculation of the quadratic quark mass correction to the correlator of the two currents relevant for the strangeness-changing semihadronic tau-decay rate is presented including its real part at the four-loop level. This allows to perform the extraction of the strange quark mass m_s from the decay width of the tau-lepton with full O(alpha_s^3) accuracy. In agreement with previous estimates the newly computed alpha_s^3 term proves to be rather large. This justifies inclusion of the similarly estimated alpha_s^4 term in phenomenological analysis. Combined with an updated value of V_{us} and an ``'improved'' version of the renormalization group improvement of the perturbative series this leads to an increase of the central value of m_s by about 20 % and a partial reduction of the theoretical uncertainty by about 50 %.